Decorrelation-Based Feature Discovery: TADPOLE-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

Data from the speech features

1.2 The data set

TADPOLE_D1_D2 <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2.csv")
TADPOLE_D1_D2_Dict <- read.csv("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict.csv")
TADPOLE_D1_D2_Dict_LR <- as.data.frame(read_excel("~/GitHub/BSWiMS/Data/TADPOLE/TADPOLE_D1_D2_Dict_LR.xlsx",sheet = "LeftRightFeatures"))


rownames(TADPOLE_D1_D2_Dict) <- TADPOLE_D1_D2_Dict$FLDNAME

1.3 Conditioning the data

# mm3 to mm
isVolume <- c("Ventricles","Hippocampus","WholeBrain","Entorhinal","Fusiform","MidTemp","ICV",
              TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Volume")]
              )


#TADPOLE_D1_D2[,isVolume] <- apply(TADPOLE_D1_D2[,isVolume],2,'^',(1/3))
TADPOLE_D1_D2[,isVolume] <- TADPOLE_D1_D2[,isVolume]^(1/3)

# mm2 to mm
isArea <- TADPOLE_D1_D2_Dict$FLDNAME[str_detect(TADPOLE_D1_D2_Dict$TEXT,"Area")]
TADPOLE_D1_D2[,isArea] <- sqrt(TADPOLE_D1_D2[,isArea])

# Get only cross sectional measurements
FreeSurfersetCross <- str_detect(colnames(TADPOLE_D1_D2),"UCSFFSX")

# The subset of baseline measurements
baselineTadpole <- subset(TADPOLE_D1_D2,VISCODE=="bl")
table(baselineTadpole$DX)

                   Dementia Dementia to MCI             MCI MCI to Dementia 
          7             336               1             864               5 
  MCI to NL              NL       NL to MCI 
          2             521               1 

table(baselineTadpole$DX_bl)

AD CN EMCI LMCI SMC 342 417 310 562 106

rownames(baselineTadpole) <- baselineTadpole$PTID


validBaselineTadpole <- cbind(DX=baselineTadpole$DX_bl,
                                 AGE=baselineTadpole$AGE,
                                 Gender=1*(baselineTadpole$PTGENDER=="Female"),
                                 ADAS11=baselineTadpole$ADAS11,
                                 ADAS13=baselineTadpole$ADAS13,
                                 MMSE=baselineTadpole$MMSE,
                                 RAVLT_immediate=baselineTadpole$RAVLT_immediate,
                                 RAVLT_learning=baselineTadpole$RAVLT_learning,
                                 RAVLT_forgetting=baselineTadpole$RAVLT_forgetting,
                                 RAVLT_perc_forgetting=baselineTadpole$RAVLT_perc_forgetting,
                                 FAQ=baselineTadpole$FAQ,
                                 Ventricles=baselineTadpole$Ventricles,
                                 Hippocampus=baselineTadpole$Hippocampus,
                                 WholeBrain=baselineTadpole$WholeBrain,
                                 Entorhinal=baselineTadpole$Entorhinal,
                                 Fusiform=baselineTadpole$Fusiform,
                                 MidTemp=baselineTadpole$MidTemp,
                                 ICV=baselineTadpole$ICV,
                                 baselineTadpole[,FreeSurfersetCross])


LeftFields <- TADPOLE_D1_D2_Dict_LR$LFN
names(LeftFields) <- LeftFields
LeftFields <- LeftFields[LeftFields %in% colnames(validBaselineTadpole)]
RightFields <- TADPOLE_D1_D2_Dict_LR$RFN
names(RightFields) <- RightFields
RightFields <- RightFields[RightFields %in% colnames(validBaselineTadpole)]

## Normalize to ICV
validBaselineTadpole$Ventricles=validBaselineTadpole$Ventricles/validBaselineTadpole$ICV
validBaselineTadpole$Hippocampus=validBaselineTadpole$Hippocampus/validBaselineTadpole$ICV
validBaselineTadpole$WholeBrain=validBaselineTadpole$WholeBrain/validBaselineTadpole$ICV
validBaselineTadpole$Entorhinal=validBaselineTadpole$Entorhinal/validBaselineTadpole$ICV
validBaselineTadpole$Fusiform=validBaselineTadpole$Fusiform/validBaselineTadpole$ICV
validBaselineTadpole$MidTemp=validBaselineTadpole$MidTemp/validBaselineTadpole$ICV

leftData <- validBaselineTadpole[,LeftFields]/validBaselineTadpole$ICV
RightData <- validBaselineTadpole[,RightFields]/validBaselineTadpole$ICV

## get mean and relative difference 
meanLeftRight <- (leftData + RightData)/2
difLeftRight <- abs(leftData - RightData)
reldifLeftRight <- difLeftRight/meanLeftRight
colnames(meanLeftRight) <- paste("M",colnames(meanLeftRight),sep="_")
colnames(difLeftRight) <- paste("D",colnames(difLeftRight),sep="_")
colnames(reldifLeftRight) <- paste("RD",colnames(reldifLeftRight),sep="_")


validBaselineTadpole <- validBaselineTadpole[,!(colnames(validBaselineTadpole) %in% 
                                               c(LeftFields,RightFields))]
validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight,reldifLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,meanLeftRight,difLeftRight)
#validBaselineTadpole <- cbind(validBaselineTadpole,leftData,RightData)

## Remove columns with too many NA more than %15 of NA
nacount <- apply(is.na(validBaselineTadpole),2,sum)/nrow(validBaselineTadpole) < 0.15
diagnose <- validBaselineTadpole$DX
pander::pander(table(diagnose))

AD	CN	EMCI	LMCI	SMC
342	417	310	562	106

validBaselineTadpole <- validBaselineTadpole[,nacount]
## Remove character columns
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole <- validBaselineTadpole[,!ischar]
## Place back diagnose
validBaselineTadpole$DX <- diagnose


validBaselineTadpole <- validBaselineTadpole[complete.cases(validBaselineTadpole),]
ischar <- sapply(validBaselineTadpole,class) == "character"
validBaselineTadpole[,!ischar] <- sapply(validBaselineTadpole[,!ischar],as.numeric)

colnames(validBaselineTadpole) <- str_remove_all(colnames(validBaselineTadpole),"_UCSFFSX_11_02_15_UCSFFSX51_08_01_16")
colnames(validBaselineTadpole) <- str_replace_all(colnames(validBaselineTadpole)," ","_")
validBaselineTadpole$LONISID <- NULL
validBaselineTadpole$IMAGEUID <- NULL
validBaselineTadpole$LONIUID <- NULL

diagnose <- as.character(validBaselineTadpole$DX)
validBaselineTadpole$DX <- diagnose
pander::pander(table(validBaselineTadpole$DX))

AD	CN	EMCI	LMCI	SMC
245	359	272	444	93

validBaselineTadpole[validBaselineTadpole$DX %in% c("EMCI","LMCI"),"DX"] <- "MCI" 
validBaselineTadpole[validBaselineTadpole$DX %in% c("CN","SMC"),"DX"] <- "NL" 

pander::pander(table(validBaselineTadpole$DX))

AD	MCI	NL
245	716	452

1.4 Get the Time To Event on MCI Subjects

subjectsID <- rownames(validBaselineTadpole)
visitsID <- unique(TADPOLE_D1_D2$VISCODE)
baseDx <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE=="bl",c("PTID","DX","EXAMDATE")]
rownames(baseDx) <- baseDx$PTID 
baseDx <- baseDx[subjectsID,]
lastDx <- baseDx
toDementia <- baseDx
table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        244               1             711               2               2 
         NL       NL to MCI 
        452               1 

hasDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]


for (vid in visitsID)
{
  DxValue <- TADPOLE_D1_D2[TADPOLE_D1_D2$VISCODE==vid,c("PTID","DX","EXAMDATE")]
  rownames(DxValue) <- DxValue$PTID 
  DxValue <- DxValue[DxValue$PTID %in% subjectsID,]
  noDX <- DxValue$PTID[nchar(DxValue$DX) < 1]
  print(length(noDX))
  DxValue[noDX,] <- lastDx[noDX,]
  inLast <- lastDx$PTID[lastDx$PTID %in% DxValue$PTID]
  print(length(inLast))
  lastDx[inLast,] <- DxValue[inLast,]
  noDementia <- !(toDementia$PTID %in% hasDementia)
  toDementia[noDementia,] <- lastDx[noDementia,]
  hasDementia <- unique(c(hasDementia,lastDx$PTID[str_detect(lastDx$DX,"Dementia")]))
}

[1] 0 [1] 1413 [1] 2 [1] 1326 [1] 6 [1] 1218 [1] 23 [1] 1095 [1] 805 [1] 1058 [1] 29 [1] 710 [1] 20 [1] 212 [1] 14 [1] 167 [1] 32 [1] 553 [1] 25 [1] 298 [1] 18 [1] 130 [1] 667 [1] 667 [1] 112 [1] 112 [1] 176 [1] 176 [1] 177 [1] 177 [1] 625 [1] 625 [1] 251 [1] 251 [1] 159 [1] 159 [1] 7 [1] 7 [1] 17 [1] 99 [1] 9 [1] 63 [1] 1 [1] 1

table(lastDx$DX)

   Dementia Dementia to MCI             MCI MCI to Dementia       MCI to NL 
        428               2             463              80               7 
         NL  NL to Dementia       NL to MCI 
        406               1              26 

baseMCI <-baseDx$PTID[baseDx$DX == "MCI"]
lastDementia <- lastDx$PTID[str_detect(lastDx$DX,"Dementia")]
lastDementia2 <- toDementia$PTID[str_detect(toDementia$DX,"Dementia")]
lastNL <- lastDx$PTID[str_detect(lastDx$DX,"NL")]

MCIatBaseline <- baseDx[baseMCI,]
MCIatEvent <- toDementia[baseMCI,]
MCIatLast <- lastDx[baseMCI,]

MCIconverters <- MCIatBaseline[baseMCI %in% lastDementia,]
MCI_No_converters <- MCIatBaseline[!(baseMCI %in% MCIconverters$PTID),]
MCIconverters$TimeToEvent <- (as.Date(toDementia[MCIconverters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCIconverters$EXAMDATE))

sum(MCIconverters$TimeToEvent ==0)

[1] 0

MCIconverters$AtEventDX <- MCIatEvent[MCIconverters$PTID,"DX"]
MCIconverters$LastDX <- MCIatLast[MCIconverters$PTID,"DX"]

MCI_No_converters$TimeToEvent <- (as.Date(lastDx[MCI_No_converters$PTID,"EXAMDATE"]) 
                                   - as.Date(MCI_No_converters$EXAMDATE))

MCI_No_converters$LastDX <- MCIatLast[MCI_No_converters$PTID,"DX"]

MCI_No_converters <- subset(MCI_No_converters,TimeToEvent > 0)

2 Prognosis MCI to AD Conversion

2.1 the set

MCIPrognosisIDs <- c(MCIconverters$PTID,MCI_No_converters$PTID)

TADPOLECrossMRI <- validBaselineTadpole[MCIPrognosisIDs,]
table(TADPOLECrossMRI$DX)

MCI 680

TADPOLECrossMRI$DX <- NULL
TADPOLECrossMRI$status <- 1*(rownames(TADPOLECrossMRI) %in% MCIconverters$PTID)
table(TADPOLECrossMRI$status)

0 1 436 244

2.1.0.1 Standarize the names for the reporting

studyName <- "TADPOLE"
dataframe <- TADPOLECrossMRI
outcome <- "status"

TopVariables <- 10

thro <- 0.60
cexheat = 0.15

2.2 Generaring the report

2.2.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

2.2.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
680	477

pander::pander(table(dataframe[,outcome]))

0	1
436	244

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

2.2.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

2.3 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

2.3.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.9996707

2.4 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  ICV D_ST17SV RD_ST56CV D_ST65SV D_ST61SV D_ST36CV 
#>             AGE          ADAS11          ADAS13            MMSE RAVLT_immediate 
#>      0.02521008      0.35924370      0.36134454      0.01890756      0.11344538 
#>  RAVLT_learning 
#>      0.07773109 
#> 
#>  Included: 476 , Uni p: 0.0003151261 , Base Size: 56 , Rcrit: 0.1307612 
#> 
#> 
 1 <R=0.918,thr=0.950>, Top: 153< 1 >.[Fa= 153 ]( 153 , 153 , 0 ),<|><>Tot Used: 306 , Added: 153 , Zero Std: 0 , Max Cor: 0.909
#> 
 2 <R=0.778,thr=0.900>, Top: 3< 1 >[Fa= 156 ]( 3 , 3 , 153 ),<|><>Tot Used: 312 , Added: 3 , Zero Std: 0 , Max Cor: 0.884
#> 
 3 <R=0.776,thr=0.800>, Top: 41< 1 >[Fa= 188 ]( 39 , 49 , 156 ),<|><>Tot Used: 359 , Added: 49 , Zero Std: 0 , Max Cor: 0.923
#> 
 4 <R=0.747,thr=0.900>, Top: 1< 1 >[Fa= 189 ]( 1 , 1 , 188 ),<|><>Tot Used: 360 , Added: 1 , Zero Std: 0 , Max Cor: 0.841
#> 
 5 <R=0.746,thr=0.800>, Top: 1< 1 >[Fa= 190 ]( 1 , 1 , 189 ),<|><>Tot Used: 362 , Added: 1 , Zero Std: 0 , Max Cor: 0.800
#> 
 6 <R=0.745,thr=0.700>, Top: 114< 1 >.[Fa= 275 ]( 112 , 120 , 190 ),<|><>Tot Used: 451 , Added: 120 , Zero Std: 0 , Max Cor: 0.748
#> 
 7 <R=0.656,thr=0.700>, Top: 1< 1 >[Fa= 276 ]( 1 , 1 , 275 ),<|><>Tot Used: 453 , Added: 1 , Zero Std: 0 , Max Cor: 0.696
#> 
 8 <R=0.654,thr=0.600>, Top: 44< 1 >[Fa= 292 ]( 43 , 59 , 276 ),<|><>Tot Used: 468 , Added: 59 , Zero Std: 0 , Max Cor: 0.680
#> 
 9 <R=0.640,thr=0.600>, Top: 3< 1 >[Fa= 294 ]( 3 , 3 , 292 ),<|><>Tot Used: 468 , Added: 3 , Zero Std: 0 , Max Cor: 0.746
#> 
 10 <R=0.746,thr=0.700>, Top: 1< 1 >[Fa= 295 ]( 1 , 1 , 294 ),<|><>Tot Used: 468 , Added: 1 , Zero Std: 0 , Max Cor: 0.599
#> 
 11 <R=0.599,thr=0.600>
#> 
 [ 11 ], 0.5988799 Decor Dimension: 468 Nused: 468 . Cor to Base: 305 , ABase: 476 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

1378

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

1286

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

0.827

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.664

varratio <- attr(DEdataframe,"VarRatio")

pander::pander(tail(varratio))

La_RD_ST61SV	La_RD_ST65SV	La_RD_ST17SV	La_RD_ST52CV	La_RD_ST129CV	La_ST10CV
0.00369	0.00358	0.00274	0.00272	0.00226	0.000658

2.4.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPLTM <- attr(DEdataframe,"UPLTM")
  
  gplots::heatmap.2(1.0*(abs(UPLTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
  
  
  
}

2.4.2 Formulas Network

Displaying the features associations

par(op)
clustable <- c("To many variables")


  transform <- attr(DEdataframe,"UPLTM") != 0
  tnames <- colnames(transform)
  colnames(transform) <- str_remove_all(colnames(transform),"La_")
  transform <- abs(transform*cor(dataframe[,rownames(transform)])) # The weights are proportional to the observed correlation
  
  
  fscore <- attr(DEdataframe,"fscore")
  VertexSize <- fscore # The size depends on the variable independence relevance (fscore)
  names(VertexSize) <- str_remove_all(names(VertexSize),"La_")
  VertexSize <- 10*(VertexSize-min(VertexSize))/(max(VertexSize)-min(VertexSize)) # Normalization

  VertexSize <- VertexSize[rownames(transform)]
  rsum <- apply(1*(transform !=0),1,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  csum <- apply(1*(transform !=0),2,sum) + 0.01*VertexSize + 0.001*varratio[tnames]
  
  ntop <- min(10,length(rsum))


  topfeatures <- unique(c(names(rsum[order(-rsum)])[1:ntop],names(csum[order(-csum)])[1:ntop]))
  rtrans <- transform[topfeatures,]
  csum <- (apply(1*(rtrans !=0),2,sum) > 1*(colnames(rtrans) %in% topfeatures))
  rtrans <- rtrans[,csum]
  topfeatures <- unique(c(topfeatures,colnames(rtrans)))
  print(ncol(transform))

[1] 468

  transform <- transform[topfeatures,topfeatures]
  print(ncol(transform))

[1] 89

  if (ncol(transform)>100)
  {
    csum <- apply(1*(transform !=0),1,sum) 
    csum <- csum[csum > 1]
    csum <- csum + 0.01*VertexSize[names(csum)]
    csum <- csum[order(-csum)]
    tpsum <- min(20,length(csum))
    trsum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
    rtrans <- transform[trsum,]
    topfeatures <- unique(c(rownames(rtrans),colnames(rtrans)))
    transform <- transform[topfeatures,topfeatures]
    if (nrow(transform) > 150)
    {
      csum <- apply(1*(rtrans != 0 ),2,sum)
      csum <- csum + 0.01*VertexSize[names(csum)]
      csum <- csum[order(-csum)]
      tpsum <- min(130,length(csum))
      csum <- rownames(transform)[rownames(transform) %in% names(csum[1:tpsum])]
      csum <- unique(c(trsum,csum))
      transform <- transform[csum,csum]
    }
    print(ncol(transform))
  }

    if (ncol(transform) < 150)
    {

      gplots::heatmap.2(transform,
                        trace = "none",
                        mar = c(5,5),
                        col=rev(heat.colors(5)),
                        main = "Red Decorrelation matrix",
                        cexRow = cexheat,
                        cexCol = cexheat,
                       srtCol=45,
                       srtRow=45,
                        key.title=NA,
                        key.xlab="|Beta|>0",
                        xlab="Output Feature", ylab="Input Feature")
  
      par(op)
      VertexSize <- VertexSize[colnames(transform)]
      gr <- graph_from_adjacency_matrix(transform,mode = "directed",diag = FALSE,weighted=TRUE)
      gr$layout <- layout_with_fr
      
#      fc <- cluster_optimal(gr)
        fc <- cluster_walktrap (gr,steps=50)
      plot(fc, gr,
           edge.width = 2*E(gr)$weight,
           vertex.size=VertexSize,
           edge.arrow.size=0.5,
           edge.arrow.width=0.5,
           vertex.label.cex=(0.15+0.05*VertexSize),
           vertex.label.dist=0.5 + 0.05*VertexSize,
           main="Top Feature Association")
      
      varratios <- varratio
      fscores <- fscore
      names(varratios) <- str_remove_all(names(varratios),"La_")
      names(fscores) <- str_remove_all(names(fscores),"La_")

      dc <- getLatentCoefficients(DEdataframe)
      theCharformulas <- attr(dc,"LatentCharFormulas")

      
      clustable <- as.data.frame(cbind(Variable=fc$names,
                                       Formula=as.character(theCharformulas[paste("La_",fc$names,sep="")]),
                                       Class=fc$membership,
                                       ResidualVariance=round(varratios[fc$names],3),
                                       Fscore=round(fscores[fc$names],3)
                                       )
                                 )
      rownames(clustable) <- str_replace_all(rownames(clustable),"__","_")
      clustable$Variable <- NULL
      clustable$Class <- as.integer(clustable$Class)
      clustable$ResidualVariance <- as.numeric(clustable$ResidualVariance)
      clustable$Fscore <- as.numeric(clustable$Fscore)
      clustable <- clustable[order(-clustable$Fscore),]
      clustable <- clustable[order(clustable$Class),]
      clustable <- clustable[clustable$Fscore >= -1,]
      topv <- min(50,nrow(clustable))
      clustable <- clustable[1:topv,]
    }

pander::pander(clustable)

	Formula	Class	ResidualVariance	Fscore
D_ST47CV	NA	1	1.000	2
RD_ST47CV	- (7.852)D_ST47CV + RD_ST47CV	1	0.011	1
M_ST47CV	+ M_ST47CV - (9.554)D_ST47CV + (1.217)RD_ST47CV	1	0.333	0
RD_ST47SA	- (9.092)D_ST47CV + RD_ST47SA	1	0.271	0
D_ST47SA	+ D_ST47SA - (2.743)D_ST47CV - (0.307)RD_ST47SA + (0.349)RD_ST47CV	1	0.006	-1
D_ST34CV	NA	2	1.000	2
RD_ST34CV	- (8.906)D_ST34CV + RD_ST34CV	2	0.009	1
M_ST34CV	+ M_ST34CV - (13.746)D_ST34CV + (1.544)RD_ST34CV	2	0.352	0
RD_ST34SA	- (8.537)D_ST34CV + RD_ST34SA	2	0.515	0
D_ST34SA	+ D_ST34SA - (2.504)D_ST34CV - (0.259)RD_ST34SA + (0.281)RD_ST34CV	2	0.007	-1
D_ST15CV	NA	3	1.000	2
RD_ST15CV	- (6.775)D_ST15CV + RD_ST15CV	3	0.008	1
M_ST15CV	+ M_ST15CV - (13.253)D_ST15CV + (1.956)RD_ST15CV	3	0.363	0
RD_ST15SA	- (7.869)D_ST15CV + RD_ST15SA	3	0.318	0
D_ST15SA	+ D_ST15SA - (2.919)D_ST15CV - (0.390)RD_ST15SA + (0.431)RD_ST15CV	3	0.006	-1
M_ST59TA	NA	4	1.000	29
M_ST129CV	- (2.509)M_ST59TA + M_ST129CV	4	0.614	2
M_ST32TA	+ M_ST32TA - (0.812)M_ST59TA	4	0.422	1
M_ST48TA	+ M_ST48TA - (0.457)M_ST59TA	4	0.570	1
M_ST52TA	+ M_ST52TA - (0.828)M_ST59TA	4	0.276	0
M_ST56TA	+ M_ST56TA - (0.792)M_ST59TA	4	0.318	0
M_ST13TA	+ M_ST13TA - (0.882)M_ST59TA	4	0.317	-1
M_ST15TA	+ M_ST15TA - (0.839)M_ST59TA	4	0.273	-1
M_ST31TA	+ M_ST31TA - (0.930)M_ST59TA	4	0.174	-1
M_ST45TA	+ M_ST45TA - (0.755)M_ST59TA	4	0.296	-1
M_ST47TA	+ M_ST47TA - (0.736)M_ST59TA	4	0.375	-1
M_ST49TA	+ M_ST49TA - (0.719)M_ST59TA	4	0.303	-1
M_ST51TA	+ M_ST51TA - (0.995)M_ST59TA	4	0.295	-1
M_ST58TA	+ M_ST58TA - (0.918)M_ST59TA	4	0.315	-1
RD_ST43TA	+ (2.424)M_ST59TA - (54.888)D_ST43TA + RD_ST43TA	4	0.019	-1
D_ST54CV	NA	5	1.000	2
RD_ST54CV	- (9.266)D_ST54CV + RD_ST54CV	5	0.013	1
M_ST54CV	+ M_ST54CV - (7.520)D_ST54CV + (0.812)RD_ST54CV	5	0.332	0
RD_ST54SA	- (9.981)D_ST54CV + RD_ST54SA	5	0.413	0
D_ST54SA	+ D_ST54SA - (3.032)D_ST54CV - (0.215)RD_ST54SA + (0.327)RD_ST54CV	5	0.012	-1
D_ST32CV	NA	6	1.000	2
RD_ST32CV	- (5.670)D_ST32CV + RD_ST32CV	6	0.008	1
M_ST32CV	+ M_ST32CV - (12.354)D_ST32CV + (2.179)RD_ST32CV	6	0.484	0
RD_ST32SA	- (5.230)D_ST32CV + RD_ST32SA	6	0.495	0
D_ST32SA	+ D_ST32SA - (2.287)D_ST32CV - (0.464)RD_ST32SA + (0.403)RD_ST32CV	6	0.005	-1
D_ST45CV	NA	7	1.000	2
RD_ST45CV	- (7.280)D_ST45CV + RD_ST45CV	7	0.008	2
RD_ST45SA	- (9.378)D_ST45CV + RD_ST45SA	7	0.228	0
M_ST45SA	+ M_ST45SA - (4.835)D_ST45SA - (5.514)D_ST45CV + (1.640)RD_ST45SA + (0.757)RD_ST45CV	7	0.370	-1
D_ST45SA	+ D_ST45SA - (3.414)D_ST45CV - (0.339)RD_ST45SA + (0.469)RD_ST45CV	7	0.007	-1
M_ST37SV	NA	8	1.000	5
Ventricles	+ Ventricles - (1.275)M_ST37SV	8	0.013	-1
ST127SV	+ ST127SV - (29.897)M_ST37SV	8	0.441	-1
ST7SV	+ ST7SV - (18.157)M_ST37SV	8	0.550	-1
RD_ST30SV	+ (0.642)M_ST37SV - (12.479)D_ST30SV + RD_ST30SV	8	0.110	-1

par(op)

2.5 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

2.6 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after ILAA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.5988799

2.7 U-MAP Visualization of features

2.7.1 The UMAP on Raw Data

  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  topvars <- univariate_BinEnsemble(dataframe,outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),dataframe,family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

ADAS11, ADAS13, RAVLT_immediate, FAQ, Hippocampus and WholeBrain

#  names(topvars)
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(dataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(dataframe[1:numsub,varlist],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])

#}

2.7.2 The decorralted UMAP

  varlistcV <- names(varratio[varratio >= 0.01])
  topvars <- univariate_BinEnsemble(DEdataframe[,varlistcV],outcome)
  lso <- LASSO_MIN(formula(paste(outcome,"~.")),DEdataframe[,varlistcV],family="binomial")
  topvars <- unique(c(names(topvars),lso$selectedfeatures))
  pander::pander(head(topvars))

FAQ, ADAS13, M_ST29SV, RAVLT_perc_forgetting, La_D_ST31CV and RAVLT_learning

  varlistcV <- varlistcV[varlistcV != outcome]
  
#  DEdataframe[,outcome] <- as.numeric(DEdataframe[,outcome])
#if (nrow(dataframe) < 1000)
#{
  datasetframe.umap = umap(scale(DEdataframe[1:numsub,topvars]),n_components=2)
#  datasetframe.umap = umap(DEdataframe[1:numsub,varlistcV],n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After ILAA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])

#}

2.8 Univariate Analysis

2.8.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : M_ST24SA 200 : D_ST49TA 300 : D_ST47CV 400 : RD_ST24SA

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_M_ST24SA 200 : D_ST49TA 300 : D_ST47CV 400 : La_RD_ST24SA

2.8.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS13	20.7611	6.16923	14.0091	5.78970	0.03549	0.788
ADAS11	12.8635	4.56128	8.7155	3.84978	0.00264	0.761
FAQ	5.4631	4.90262	1.9266	2.98257	0.00000	0.756
M_ST40CV	0.1799	0.00875	0.1875	0.00763	0.28199	0.750
M_ST29SV	0.1253	0.00708	0.1321	0.00750	0.58088	0.745
M_ST12SV	0.0913	0.00535	0.0962	0.00550	0.50030	0.744
Hippocampus	0.1582	0.00886	0.1664	0.00945	0.44340	0.737
RAVLT_immediate	29.0205	7.69236	37.2798	10.92838	0.04406	0.728
M_ST24CV	0.0996	0.00800	0.1059	0.00706	0.04673	0.727
M_ST31CV	0.1910	0.00945	0.1986	0.00902	0.94566	0.717

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
ADAS13	20.761066	6.17e+00	14.009106	5.79e+00	3.55e-02	0.788
FAQ	5.463115	4.90e+00	1.926606	2.98e+00	0.00e+00	0.756
M_ST29SV	0.125302	7.08e-03	0.132097	7.50e-03	5.81e-01	0.745
La_RD_ST40CV	0.000721	3.70e-03	-0.001552	2.58e-03	2.53e-06	0.718
RAVLT_perc_forgetting	74.353614	2.92e+01	52.421164	3.14e+01	1.42e-03	0.700
La_RD_ST12SV	0.000499	3.05e-03	-0.001192	3.04e-03	1.28e-12	0.697
La_D_ST31CV	-0.000036	8.45e-04	0.000474	7.12e-04	1.64e-02	0.696
La_M_ST24CV	0.100098	5.62e-03	0.103429	4.96e-03	1.78e-01	0.691
La_RD_ST26CV	0.000512	2.25e-03	-0.000811	2.08e-03	1.64e-07	0.690
La_RD_ST58CV	0.000413	2.10e-03	-0.000648	1.46e-03	2.45e-06	0.687

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
2.64	337	0.706

theCharformulas <- attr(dc,"LatentCharFormulas")

topvar <- rownames(tableRaw)
finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]
finalTable$varratio <- varratio[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores","varratio")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores	varratio
ADAS13	NA	20.761066	6.17e+00	14.009106	5.79e+00	3.55e-02	0.788	0.788	2	1.00000
ADAS11	NA	12.863525	4.56e+00	8.715528	3.85e+00	2.64e-03	0.761	0.761	NA	NA
FAQ	NA	5.463115	4.90e+00	1.926606	2.98e+00	0.00e+00	0.756	0.756	0	1.00000
M_ST40CV	NA	0.179856	8.75e-03	0.187527	7.63e-03	2.82e-01	0.750	0.750	NA	NA
M_ST29SV	NA	0.125302	7.08e-03	0.132097	7.50e-03	5.81e-01	0.745	0.745	6	1.00000
M_ST12SV	NA	0.091327	5.35e-03	0.096219	5.50e-03	5.00e-01	0.744	0.744	NA	NA
Hippocampus	NA	0.158226	8.86e-03	0.166444	9.45e-03	4.43e-01	0.737	0.737	NA	NA
RAVLT_immediate	NA	29.020492	7.69e+00	37.279817	1.09e+01	4.41e-02	0.728	0.728	NA	NA
M_ST24CV	NA	0.099630	8.00e-03	0.105940	7.06e-03	4.67e-02	0.727	0.727	NA	NA
La_RD_ST40CV	- (5.536)D_ST40CV + RD_ST40CV	0.000721	3.70e-03	-0.001552	2.58e-03	2.53e-06	0.718	0.585	1	0.00851
M_ST31CV	NA	0.191026	9.45e-03	0.198568	9.02e-03	9.46e-01	0.717	0.717	NA	NA
RAVLT_perc_forgetting	NA	74.353614	2.92e+01	52.421164	3.14e+01	1.42e-03	0.700	0.700	1	1.00000
La_RD_ST12SV	- (10.875)D_ST12SV + RD_ST12SV	0.000499	3.05e-03	-0.001192	3.04e-03	1.28e-12	0.697	0.552	-1	0.01050
La_D_ST31CV	+ D_ST31CV - (0.191)RD_ST31CV	-0.000036	8.45e-04	0.000474	7.12e-04	1.64e-02	0.696	0.511	1	0.01070
La_M_ST24CV	+ M_ST24CV - (8.320)D_ST24CV + (0.827)RD_ST24CV	0.100098	5.62e-03	0.103429	4.96e-03	1.78e-01	0.691	0.727	-1	0.46302
La_RD_ST26CV	- (5.692)D_ST26CV + RD_ST26CV	0.000512	2.25e-03	-0.000811	2.08e-03	1.64e-07	0.690	0.534	0	0.00632
La_RD_ST58CV	- (5.448)D_ST58CV + RD_ST58CV	0.000413	2.10e-03	-0.000648	1.46e-03	2.45e-06	0.687	0.554	1	0.00596

2.9 Comparing ILAA vs PCA vs EFA

2.9.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE,tol=0.01)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

2.9.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)-1)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

2.10 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	330	106
1	36	208

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.791	0.759	0.821
3	se	0.852	0.802	0.894
4	sp	0.757	0.714	0.796
6	diag.or	17.987	11.866	27.267

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe[,c(outcome,varlistcV)],control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="ILAA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	396	40
1	109	135

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.781	0.748	0.811
3	se	0.553	0.489	0.617
4	sp	0.908	0.877	0.934
6	diag.or	12.261	8.124	18.506

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	399	37
1	135	109

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.747	0.713	0.779
3	se	0.447	0.383	0.511
4	sp	0.915	0.885	0.940
6	diag.or	8.707	5.716	13.263

par(op)

2.10.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	365	71
1	77	167

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.782	0.749	0.813
3	se	0.684	0.622	0.742
4	sp	0.837	0.799	0.871
6	diag.or	11.150	7.695	16.155

  par(op)